论文标题
通过广泛的Plackett-luce模型对等级有序数据进行建模和分析
Modelling and analysis of rank ordered data with ties via a generalized Plackett-Luce model
论文作者
论文摘要
提出了一个带有领带的等级排序数据的简单生成模型。该模型基于订购几何潜在变量，可以看作是Plackett-luce（PL）模型的离散对应物，这是一种流行的，相对可拖延的置换模型。该模型将被称为GPL模型，用于广义（或几何）Plackett-luce模型，其中包含PL模型作为限制特殊情况。得出了可能性的封闭形式表达式。通过数据增强着眼于贝叶斯推断，对于多重比较的一般情况和配对比较的特殊情况，都会得出简单的Gibbs采样和EM算法。该方法应用于几个真实的数据示例。这些示例突出了GPL模型应对一系列数据类型的灵活性，推论算法的简单性和效率以及GPL模型由于其简单生成构建而自然促进预测推断的能力。
A simple generative model for rank ordered data with ties is presented. The model is based on ordering geometric latent variables and can be seen as the discrete counterpart of the Plackett-Luce (PL) model, a popular, relatively tractable model for permutations. The model, which will be referred to as the GPL model, for generalized (or geometric) Plackett-Luce model, contains the PL model as a limiting special case. A closed form expression for the likelihood is derived. With a focus on Bayesian inference via data augmentation, simple Gibbs sampling and EM algorithms are derived for both the general case of multiple comparisons and the special case of paired comparisons. The methodology is applied to several real data examples. The examples highlight the flexibility of the GPL model to cope with a range of data types, the simplicity and efficiency of the inferential algorithms, and the ability of the GPL model to naturally facilitate predictive inference due to its simple generative construction.
